- Email: [email protected]
Correlation between solar flare productivity and photospheric vector magnetic fields
Advances in Space Research 42 (2008) 1475–1479 www.elsevier.com/locate/asr
Correlation between solar flare productivity and photospheric vector magnetic fields q Yanmei Cui *, Huaning Wang National Astronomical Observatories of China, Chinese Academy of Sciences, Beijing 100012, China Received 31 October 2006; received in revised form 23 May 2007; accepted 28 June 2007
Abstract Studying the statistical correlation between the solar flare productivity and photospheric magnetic fields is very important and necessary. It is helpful to set up a practical flare forecast model based on magnetic properties and improve the physical understanding of solar flare eruptions. In the previous study ([Cui, Y.M., Li, R., Zhang, L.Y., He, Y.L., Wang, H.N. Correlation between solar flare productivity and photospheric magnetic field properties 1. Maximum horizontal gradient, length of neutral line, number of singular points. Sol. Phys. 237, 45–59, 2006]; from now on we refer to this paper as ‘Paper I’), three measures of the maximum horizontal gradient, the length of the neutral line, and the number of singular points are computed from 23990 SOHO/MDI longitudinal magnetograms. The statistical relationship between the solar flare productivity and these three measures is well fitted with sigmoid functions. In the current work, the three measures of the length of strong-shear neutral line, total unsigned current, and total unsigned current helicity are computed from 1353 vector magnetograms observed at Huairou Solar Observing Station. The relationship between the solar flare productivity and the current three measures can also be well fitted with sigmoid functions. These results are expected to be beneficial to future operational flare forecasting models. 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Solar flare productivity; Vector magnetic fields; Magnetic measures
1. Introduction It is widely believed that solar flares are physically related with the magnetic complexity and non-potentiality, which are conventionally described with some parameters such as the magnetic shear angle (Hagyard et al., 1984; Schmieder et al., 1994; Wang et al., 1994a,b), the horizontal gradient of longitudinal magnetic fields (Zirin and Wang, 1993; Zhang et al., 1994; Tian et al., 2002), the elecq
Thanks to the referees for a lot of helpful suggestions. This work is supported by National Natural Science Foundation of China (NSFC) under Grant 10233050 and 10673017, by Chinese Academy of Sciences through Grant KGCX3-SYW-403-10, and by National Ministry of Science and Technology under Grant 2006CB806307. Acknowledge the HSOS and GOES teams for providing data. * Corresponding author. Tel.: +86 10 64888756. E-mail addresses: [email protected] (Y. Cui), [email protected] (H. Wang).
tric current (Canfield et al., 1993; Lin et al., 1993; Wang et al., 1994a,b), etc. However, how the magnetic complexity and non-potentiality trigger solar flares remains unknown. For this reason, solar flare forecasting models still mainly depend on the statistical relationship between the flare production and the sunspot morphological evolutions (McIntosh, 1990; Gallagher et al., 2002). Leka and Barnes (2003a,b) analyzed the statistical relationship of solar flares with several parameters concerning the magnetic complexity and non-potentiality and pointed out that it is possible to distinguish between an event-imminent photospheric magnetic state and an event-quiet state only by considering multiple measures simultaneously. Their results should be further confirmed since they only analyzed a limited number of samples (only one or several cases). In order to improve operational flare forecasting models, it is important and necessary to study the correlation
0273-1177/$34.00 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.06.071
1476
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
between solar flares and photospheric magnetic fields with a large number of statistical samples. In Paper I, by employing SOHO/MDI longitudinal magnetograms containing 870 active regions, we investigated the relationship between the solar flare productivity (SFP) and magnetic measures including the maximum horizontal gradient, the length of the neutral line, and the number of singular points. Our statistical results suggested that this relationship can be well fitted with sigmoid functions. Nevertheless, MDI cannot offer magnetic transverse components such that the computation of physical properties such as shear and current is limited. Vector magnetograms can provide more information about the magnetic complexity and non-potentiality for longitudinal and transverse fields, and hence are expected to give better predictions on the SFP. With a large number of vector magnetograms observed at Huairou Solar Observing Station (HSOS), we studied the relationship between the SFP and three measures including strong-shear neutral line, total unsigned current, and total unsigned current helicity. The data will be described in Section 2. The statistical analysis will be given in Section 3. And the results will be presented in the last section.
et al., 2002, 2003). For an active region only one magnetogram is chosen per day. During the time period January 1, 1996 to August 24, 2001, 1353 vector magnetograms containing 554 active regions are selected. Fig. 1 (top) shows one of vector magnetograms for the active region NOAA8602 on June 30, 1996. In addition, the condition ‘at least one C1.0 flare’ for selecting active regions in Paper I is not considered anymore in this study. Since each full disk MDI magnetograms often contains several active regions, we selected those regions for Paper I with at least C1.0 flare to reduce the amount of samples which can be regarded as true ‘active’ regions. On the other hand, each HSOS magnetograms is
2. Data reduction The solar photospheric vector magnetograms were observed with the Solar Magnetic Field Telescope at Huairou Solar Observing Station (HSOS) (Ai and Hu, 1986), which have a field of view about 5.23 0 · 3.63 0 . The temporal and spatial resolution of the HSOS vector magnetograms depends on the number of video frames that are added to produce them. Each magnetogram used in this paper is the sum of 256 individual frames for both line-of-sight and transverse fields, corresponding to a temporal resolution of about 5 min and a spatial resolution of 200 · 200 after a smooth average of 3 · 4 pixels to the Stokes parameters Q, U, and V. A detailed magnetic field introduction and other particulars of the stokes parameter calculation can be referred to Zhang et al. (1994), Wang et al. (1996), and Bao et al. (1999). The noise level of the line-ofsight magnetic field is comparable to the MDI noise level (20 G) and the noise level of the transverse field about 100 G. For the transverse component of the magnetic field, the 180 degree ambiguity is resolved by a potential field model, which used a Fast Fourier Transform method with the longitudinal magnetic field as the boundary condition. The data for X-ray flares are from GOES, downloaded from http://www.ngdc.noaa.gov/stp/ SOLAR/ftpsolarflares.html#xray. The criteria for the vector magnetogram selection are as follows: (i) observed during Beijing time period 11:00– 16:00 (19:00–24:00 UT) around noontime when there are usually good seeing condition in HSOS; (ii) located within 30 degrees of the solar disk center where projection effects are small enough to have little influences on solar magnetic field measurements (Gary and Hagyard, 1990; Falconer
Fig. 1. Active region NOAA8602 observed in Huairou Solar Observing Station, Beijing on June 30, 1996. Top: the background is the gray map of longitudinal magnetic field; the short bars represent the transverse fields with a 180 degree ambiguity; the black bold lines are neutral lines. Bottom: the black patches are the locations of strong shear (the shear angle larger than 40 degrees) in the vicinities of the neutral lines where the transverse field strength is larger than 300 G; the arrows denote the directions of transverse fields, which is resolved by a potential field method. The levels of isogauss contours are ±80, 160, 640, 960, 1280, 1600 G. The field of view is about 5.23 0 · 3.63 0 .
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
focused on individual active regions which are active enough to be monitored by observers.
3.1. Measures Three measures of the length of strong-shear neutral line, Ls, the total unsigned current, Itot, and the total unsigned current helicity, Htot, are employed for our statistical work. Solar flares often occur near neutral lines with strong shear (Zirin and Liggett, 1987; Gary and Hagyard, 1990; Wang et al., 1994a,b). The shear angle is defined as the azimuth difference at the photosphere between the potential transverse field, which fit the boundary conditions imposed by the observed line-of-sight fields, and the observed transverse fields (Hagyard et al., 1984). Here, Ls is the length of neutral line having the shear angle larger than 40 degrees. In a magnetogram it is hard to get the ideal neutral line due to the grid size and the noise level. For convenience, Ls is measured by the number of grids located in vicinities of the neutral line. Additionally, it is noted that Ls is different from L in Paper I, which is the length of neutral line with the strong horizontal gradient. The electric current offers the information of freeenergy stored in magnetic fields. The vertical current density, Jz, can be inferred from vector magnetic fields: 1 #By #Bx Jz ¼ ; ð1Þ l0 #x #y 1
where l0 = 4p · 10 Gm A . Itot is the area integral for absolute values of Jz, X I tot ¼ jJ z jdA: ð2Þ The current helicity describes the complexity of magnetic fields and relates to the solar flare production (Bao et al., 1999; Zhang, 2002; Abramenko, 2003). The current helicity density, hc, is measured by hc ¼ l0 Bz J z :
3.2. Total flare importance and solar flare productivity In Paper I, we have defined the total flare importance and the SFP. Within a certain time interval, the total importance for flares is, X X X X Bþ C þ 10 M þ 100 X; IMPtot ¼ 0:1
3. Analysis and results
3
1477
ð3Þ
Htot is obtained by integrating the area with absolute values of hc, X jhc jdA: ð4Þ H tot ¼ It is noted that to minimize the influence of noise, these three measures are calculated only for positions where the strength of transverse magnetic fields is larger than 300 G (the triple of the transverse noise level) and the strength of line-of-sight components larger than 20 G (the line-of-sight noise level). Fig. 1 (bottom) shows the locations of strong shear (the shear angle larger than 40 degrees) in the vicinities of the neutral lines where the transverse field strength is larger than 300 G.
ð5Þ where B, C, M, X are the intensities of B-, C-, M-, X-class X-ray flare events, respectively. The time interval is designed to be 48 h forward looking period. In the study, we focused on the PC1.0 X-ray flare production and therefore active samples satisfy IMPtot P 1. This is why Eq. (5) has to include the term of B-class flares, which is different from that in Paper I. The SFP is defined as, P ðxÞ ¼ pðx P x0 Þ ¼
S A ðxÞ ; S T ðxÞ
ð6Þ
where x is a random value of the non-potentiality or complexity measures. SA(x) is the number of the active samples and ST(x) is the number of the total samples. When x0 equals a series of values for Ls, Itot, or Htot, the number of active samples and the number of total ones can be obtained and the values of SFP can be also obtained. 3.3. Analysis and results In our work, x0 takes 0, 25, 50, 75, 100, 125, 150, 175, 200, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500 grids for Ls; x0 takes 0, 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 2.8, 3.2, 3.6, 4.0, 4.4, 4.8, 5.2, 5.6,6.0, 6.4, 6.8 · 1013 A for Itot; x0 takes 0, 1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0, 13.5, 15.0, 16.5, 18.0, 19.5, 21.0, 22.5, 24.0, 25.5 · 1013 G2 for Htot. Fig. 2 shows the distributions of the total samples and the active ones in the left panels and the corresponding values of the SFP with data points ‘+’ and the fitting curves with the sigmoid function in the right panels. The sigmoid function is in Boltzmann style, Y ¼ A2 þ
A1 A2 : 1 þ expððX X 0Þ=W Þ
ð7Þ
The four parameters of fitted sigmoid functions are shown in Table 1. In Fig. 2 (left), it can be seen that the active samples have a higher probability falling into those bins with larger values of the measures (Ls, Itot, Htot) than the total samples. That is to say, the larger the values of the three measures are, the more frequently solar flares occur. The sigmoid fitting curves in Fig. 2 (right) quantitatively describe the relationship between the SFP and the measures of Ls, Itot, Htot, which are closely correlated.
1478
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
Fig. 2. The relationship between the flare productivity in 48 h time period and the three measures of the length of strong-shear neutral line Ls, the total unsigned current Itot, and the total unsigned current helicity Htot. In the left panels, the histograms of total samples and active ones are presented when Ls, Itot, and Htot are larger than a series of values, respectively; in the right panels, the data points ‘+’ show the corresponding values of the flare productivity and the lines are Boltzmann sigmoidal fitting curves to these points.
Table 1 Four parameters of fitted sigmoid functions
Ls Itot Htot
A1
A2
X0
W
3.4423 1.7934 0.0403
1.0231 1.0212 1.0216
473.88 6.7584 3.4940
259.73 5.4383 8.9485
4. Conclusions and discussions The length of strong-shear neutral line Ls, the total unsigned current Itot, and the total unsigned current helic-
ity Htot are computed from 1353 vector magnetograms observed at HSOS, which quantitatively describe the magnetic complexity and non-potentiality. From the statistical results of the relationship between the SFP and the measures of Ls, Itot, Htot, and the sigmoid fitting curves, we can conclude that the SFP are positively correlated with the magnetic complexity and non-potentiality. This point is consistent with that of Paper I. Among Ls, Itot, and Htot, which measure is the most sensitive to the SFP? Perhaps the differential coefficient of the SFP to the measures is an evaluation criteria. Since these
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
three measures have different units, how to rescale them into new measures with the same unit need to be further considered. In Paper I, we obtained that the productivity of higher X-ray class flares is smaller than that of lower X-ray class flares. Therefore, it is natural that the values of the SFP for P C1.0 in this study are relative larger than those values for P C5.0, M1.0, M5.0, and X1.0 flares in Paper I. Additionally, we are very interested in why the statistical relationship between solar flares and magnetic properties can be well fitted by a sigmoid function. In the next step, we should provide explanations for the physical meanings of these functions, which is beneficial to set up operational flare forecast models. References Abramenko, V. Pre-flare changes in current helicity and turbulent regime of the photospheric magnetic field. Adv. Space Res. 32, 1937–1942, 2003. Ai, G., Hu, Y. The propose for the solar magnetic field telescope and its working theorem. Publ. Beijing Astron. Obs. 8, 1–10 (in Chinese), 1986. Bao, S.D., Zhang, H.Q., Ai, G.X., Zhang, M. A survey of flares and current helicity in active regions. Astron. Astrophys. Suppl. Ser. 139, 311–320, 1999. Canfield, R.C., de La Beaujardiere, J.-F., Fan, Yuhong, et al. The morphology of flare phenomena, magnetic fields, and electric currents in active regions. I – Introduction and methods. Astrophys. J. 411, 362–369 , 1993. Cui, Y.M., Li, R., Zhang, L.Y., He, Y.L., Wang, H.N. Correlation between solar flare productivity and photospheric magnetic field properties 1. Maximum horizontal gradient, length of neutral line, number of singular points. Sol. Phys. 237, 45–59, 2006. Falconer, D.A., Moore, R.L., Gary, G.A. Correlation of the coronal mass ejection productivity of solar active regions with measures of their global nonpotentiality from vector magnetograms: baseline result. Astrophys. J. 569, 1016–1025, 2002. Falconer, D.A., Moore, R.L., Gary, G.A. A measure from line-of-sight magnetograms for prediction of coronal mass ejections. J. Geophys. Res. 108 (A10), 1380–1385, 2003.
1479
Gallagher, P.T., Moon, Y.-J., Wang, H. Active-region monitoring and flare forecasting I. Data processing and first results. Sol. Phys. 209, 171–183, 2002. Gary, G.A., Hagyard, M.J. Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity. Sol. Phys. 126, 21–36, 1990. Hagyard, M.J., Smith Jr., J.B., Teuber, D., West, E.A. A quantitative study relating observed shear in photospheric magnetic fields to repeated flaring. Sol. Phys. 91, 115–126, 1984. Leka, K.D., Barnes, G. Photospheric magnetic field properties of flaring versus flare-quiet active regions. i. Data, general approach, and sample results. Astrophys. J. 595, 1277–1295, 2003a. Leka, K.D., Barnes, G. Photospheric magnetic field properties of flaring versus flare-quiet active regions. ii. Discriminant analysis. Astophys. J. 585, 1296–1306, 2003b. Lin, Y.Z., Wei, X.L., Zhang, H.Q. Variations of magnetic fields and electric currents associated with a solar flare. Sol. Phys. 148, 133–138, 1993. McIntosh, P.S. The classification of sunspot groups. Sol. Phys. 125, 251– 267, 1990. Schmieder, B., Hagyard, M.J., Ai, G.X., Zhang, H.Q., Kalman, B., Gyori, L., Rompolt, B., Demoulin, P., Machado, M.E. Relationship between magnetic field evolution and flaring sites in AR 6659 in June 1991. Sol. Phys. 150, 199–219, 1994. Tian, L., Wang, J., Wu, D. Non-potentiality of the magnetic field beneath the eruptive filament in the bastille event. Sol. Phys. 209, 375–389, 2002. Wang, H., Ewell, M., Zirin, H., Ai, G. Vector magnetic field changes associated with X-class flares. Astrophys. J. 424, 436–443, 1994a. Wang, T.J., Xu, A., Zhang, H.Q. Evolution of vector magnetic fields and vertical currents and their relationship with solar flares in AR 5747. Sol. Phys. 155, 99–112, 1994b. Wang, J., Shi, Z., Wang, H., Lu¨, Y. Flares and the magnetic nonpotentiality. Astophys. J. 456, 861–878, 1996. Zhang, H.Q., Ai, G., Yan, X., Li, W., Liu, Y. Evolution of vector magnetic field and white-light flares in a solar active region (NOAA 6659) in 1991 June. Astrophys. J. 423, 828–846, 1994. Zhang, H.Q. Magnetic field, helicity and the 2000 July 14 flare in solar active region 9077. MNRAS 332, 500–512, 2002. Zirin, H., Liggett, M.A. Delta spots and great flares. Sol. Phys. 113, 267– 281, 1987. Zirin, H., Wang, H. Strong transverse fields in delta-spots. Sol. Phys. 144, 37–43, 1993.
Correlation between solar flare productivity and photospheric vector magnetic fields q Yanmei Cui *, Huaning Wang National Astronomical Observatories of China, Chinese Academy of Sciences, Beijing 100012, China Received 31 October 2006; received in revised form 23 May 2007; accepted 28 June 2007
Abstract Studying the statistical correlation between the solar flare productivity and photospheric magnetic fields is very important and necessary. It is helpful to set up a practical flare forecast model based on magnetic properties and improve the physical understanding of solar flare eruptions. In the previous study ([Cui, Y.M., Li, R., Zhang, L.Y., He, Y.L., Wang, H.N. Correlation between solar flare productivity and photospheric magnetic field properties 1. Maximum horizontal gradient, length of neutral line, number of singular points. Sol. Phys. 237, 45–59, 2006]; from now on we refer to this paper as ‘Paper I’), three measures of the maximum horizontal gradient, the length of the neutral line, and the number of singular points are computed from 23990 SOHO/MDI longitudinal magnetograms. The statistical relationship between the solar flare productivity and these three measures is well fitted with sigmoid functions. In the current work, the three measures of the length of strong-shear neutral line, total unsigned current, and total unsigned current helicity are computed from 1353 vector magnetograms observed at Huairou Solar Observing Station. The relationship between the solar flare productivity and the current three measures can also be well fitted with sigmoid functions. These results are expected to be beneficial to future operational flare forecasting models. 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Solar flare productivity; Vector magnetic fields; Magnetic measures
1. Introduction It is widely believed that solar flares are physically related with the magnetic complexity and non-potentiality, which are conventionally described with some parameters such as the magnetic shear angle (Hagyard et al., 1984; Schmieder et al., 1994; Wang et al., 1994a,b), the horizontal gradient of longitudinal magnetic fields (Zirin and Wang, 1993; Zhang et al., 1994; Tian et al., 2002), the elecq
Thanks to the referees for a lot of helpful suggestions. This work is supported by National Natural Science Foundation of China (NSFC) under Grant 10233050 and 10673017, by Chinese Academy of Sciences through Grant KGCX3-SYW-403-10, and by National Ministry of Science and Technology under Grant 2006CB806307. Acknowledge the HSOS and GOES teams for providing data. * Corresponding author. Tel.: +86 10 64888756. E-mail addresses: [email protected] (Y. Cui), [email protected] (H. Wang).
tric current (Canfield et al., 1993; Lin et al., 1993; Wang et al., 1994a,b), etc. However, how the magnetic complexity and non-potentiality trigger solar flares remains unknown. For this reason, solar flare forecasting models still mainly depend on the statistical relationship between the flare production and the sunspot morphological evolutions (McIntosh, 1990; Gallagher et al., 2002). Leka and Barnes (2003a,b) analyzed the statistical relationship of solar flares with several parameters concerning the magnetic complexity and non-potentiality and pointed out that it is possible to distinguish between an event-imminent photospheric magnetic state and an event-quiet state only by considering multiple measures simultaneously. Their results should be further confirmed since they only analyzed a limited number of samples (only one or several cases). In order to improve operational flare forecasting models, it is important and necessary to study the correlation
0273-1177/$34.00 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.06.071
1476
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
between solar flares and photospheric magnetic fields with a large number of statistical samples. In Paper I, by employing SOHO/MDI longitudinal magnetograms containing 870 active regions, we investigated the relationship between the solar flare productivity (SFP) and magnetic measures including the maximum horizontal gradient, the length of the neutral line, and the number of singular points. Our statistical results suggested that this relationship can be well fitted with sigmoid functions. Nevertheless, MDI cannot offer magnetic transverse components such that the computation of physical properties such as shear and current is limited. Vector magnetograms can provide more information about the magnetic complexity and non-potentiality for longitudinal and transverse fields, and hence are expected to give better predictions on the SFP. With a large number of vector magnetograms observed at Huairou Solar Observing Station (HSOS), we studied the relationship between the SFP and three measures including strong-shear neutral line, total unsigned current, and total unsigned current helicity. The data will be described in Section 2. The statistical analysis will be given in Section 3. And the results will be presented in the last section.
et al., 2002, 2003). For an active region only one magnetogram is chosen per day. During the time period January 1, 1996 to August 24, 2001, 1353 vector magnetograms containing 554 active regions are selected. Fig. 1 (top) shows one of vector magnetograms for the active region NOAA8602 on June 30, 1996. In addition, the condition ‘at least one C1.0 flare’ for selecting active regions in Paper I is not considered anymore in this study. Since each full disk MDI magnetograms often contains several active regions, we selected those regions for Paper I with at least C1.0 flare to reduce the amount of samples which can be regarded as true ‘active’ regions. On the other hand, each HSOS magnetograms is
2. Data reduction The solar photospheric vector magnetograms were observed with the Solar Magnetic Field Telescope at Huairou Solar Observing Station (HSOS) (Ai and Hu, 1986), which have a field of view about 5.23 0 · 3.63 0 . The temporal and spatial resolution of the HSOS vector magnetograms depends on the number of video frames that are added to produce them. Each magnetogram used in this paper is the sum of 256 individual frames for both line-of-sight and transverse fields, corresponding to a temporal resolution of about 5 min and a spatial resolution of 200 · 200 after a smooth average of 3 · 4 pixels to the Stokes parameters Q, U, and V. A detailed magnetic field introduction and other particulars of the stokes parameter calculation can be referred to Zhang et al. (1994), Wang et al. (1996), and Bao et al. (1999). The noise level of the line-ofsight magnetic field is comparable to the MDI noise level (20 G) and the noise level of the transverse field about 100 G. For the transverse component of the magnetic field, the 180 degree ambiguity is resolved by a potential field model, which used a Fast Fourier Transform method with the longitudinal magnetic field as the boundary condition. The data for X-ray flares are from GOES, downloaded from http://www.ngdc.noaa.gov/stp/ SOLAR/ftpsolarflares.html#xray. The criteria for the vector magnetogram selection are as follows: (i) observed during Beijing time period 11:00– 16:00 (19:00–24:00 UT) around noontime when there are usually good seeing condition in HSOS; (ii) located within 30 degrees of the solar disk center where projection effects are small enough to have little influences on solar magnetic field measurements (Gary and Hagyard, 1990; Falconer
Fig. 1. Active region NOAA8602 observed in Huairou Solar Observing Station, Beijing on June 30, 1996. Top: the background is the gray map of longitudinal magnetic field; the short bars represent the transverse fields with a 180 degree ambiguity; the black bold lines are neutral lines. Bottom: the black patches are the locations of strong shear (the shear angle larger than 40 degrees) in the vicinities of the neutral lines where the transverse field strength is larger than 300 G; the arrows denote the directions of transverse fields, which is resolved by a potential field method. The levels of isogauss contours are ±80, 160, 640, 960, 1280, 1600 G. The field of view is about 5.23 0 · 3.63 0 .
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
focused on individual active regions which are active enough to be monitored by observers.
3.1. Measures Three measures of the length of strong-shear neutral line, Ls, the total unsigned current, Itot, and the total unsigned current helicity, Htot, are employed for our statistical work. Solar flares often occur near neutral lines with strong shear (Zirin and Liggett, 1987; Gary and Hagyard, 1990; Wang et al., 1994a,b). The shear angle is defined as the azimuth difference at the photosphere between the potential transverse field, which fit the boundary conditions imposed by the observed line-of-sight fields, and the observed transverse fields (Hagyard et al., 1984). Here, Ls is the length of neutral line having the shear angle larger than 40 degrees. In a magnetogram it is hard to get the ideal neutral line due to the grid size and the noise level. For convenience, Ls is measured by the number of grids located in vicinities of the neutral line. Additionally, it is noted that Ls is different from L in Paper I, which is the length of neutral line with the strong horizontal gradient. The electric current offers the information of freeenergy stored in magnetic fields. The vertical current density, Jz, can be inferred from vector magnetic fields: 1 #By #Bx Jz ¼ ; ð1Þ l0 #x #y 1
where l0 = 4p · 10 Gm A . Itot is the area integral for absolute values of Jz, X I tot ¼ jJ z jdA: ð2Þ The current helicity describes the complexity of magnetic fields and relates to the solar flare production (Bao et al., 1999; Zhang, 2002; Abramenko, 2003). The current helicity density, hc, is measured by hc ¼ l0 Bz J z :
3.2. Total flare importance and solar flare productivity In Paper I, we have defined the total flare importance and the SFP. Within a certain time interval, the total importance for flares is, X X X X Bþ C þ 10 M þ 100 X; IMPtot ¼ 0:1
3. Analysis and results
3
1477
ð3Þ
Htot is obtained by integrating the area with absolute values of hc, X jhc jdA: ð4Þ H tot ¼ It is noted that to minimize the influence of noise, these three measures are calculated only for positions where the strength of transverse magnetic fields is larger than 300 G (the triple of the transverse noise level) and the strength of line-of-sight components larger than 20 G (the line-of-sight noise level). Fig. 1 (bottom) shows the locations of strong shear (the shear angle larger than 40 degrees) in the vicinities of the neutral lines where the transverse field strength is larger than 300 G.
ð5Þ where B, C, M, X are the intensities of B-, C-, M-, X-class X-ray flare events, respectively. The time interval is designed to be 48 h forward looking period. In the study, we focused on the PC1.0 X-ray flare production and therefore active samples satisfy IMPtot P 1. This is why Eq. (5) has to include the term of B-class flares, which is different from that in Paper I. The SFP is defined as, P ðxÞ ¼ pðx P x0 Þ ¼
S A ðxÞ ; S T ðxÞ
ð6Þ
where x is a random value of the non-potentiality or complexity measures. SA(x) is the number of the active samples and ST(x) is the number of the total samples. When x0 equals a series of values for Ls, Itot, or Htot, the number of active samples and the number of total ones can be obtained and the values of SFP can be also obtained. 3.3. Analysis and results In our work, x0 takes 0, 25, 50, 75, 100, 125, 150, 175, 200, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500 grids for Ls; x0 takes 0, 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 2.8, 3.2, 3.6, 4.0, 4.4, 4.8, 5.2, 5.6,6.0, 6.4, 6.8 · 1013 A for Itot; x0 takes 0, 1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0, 13.5, 15.0, 16.5, 18.0, 19.5, 21.0, 22.5, 24.0, 25.5 · 1013 G2 for Htot. Fig. 2 shows the distributions of the total samples and the active ones in the left panels and the corresponding values of the SFP with data points ‘+’ and the fitting curves with the sigmoid function in the right panels. The sigmoid function is in Boltzmann style, Y ¼ A2 þ
A1 A2 : 1 þ expððX X 0Þ=W Þ
ð7Þ
The four parameters of fitted sigmoid functions are shown in Table 1. In Fig. 2 (left), it can be seen that the active samples have a higher probability falling into those bins with larger values of the measures (Ls, Itot, Htot) than the total samples. That is to say, the larger the values of the three measures are, the more frequently solar flares occur. The sigmoid fitting curves in Fig. 2 (right) quantitatively describe the relationship between the SFP and the measures of Ls, Itot, Htot, which are closely correlated.
1478
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
Fig. 2. The relationship between the flare productivity in 48 h time period and the three measures of the length of strong-shear neutral line Ls, the total unsigned current Itot, and the total unsigned current helicity Htot. In the left panels, the histograms of total samples and active ones are presented when Ls, Itot, and Htot are larger than a series of values, respectively; in the right panels, the data points ‘+’ show the corresponding values of the flare productivity and the lines are Boltzmann sigmoidal fitting curves to these points.
Table 1 Four parameters of fitted sigmoid functions
Ls Itot Htot
A1
A2
X0
W
3.4423 1.7934 0.0403
1.0231 1.0212 1.0216
473.88 6.7584 3.4940
259.73 5.4383 8.9485
4. Conclusions and discussions The length of strong-shear neutral line Ls, the total unsigned current Itot, and the total unsigned current helic-
ity Htot are computed from 1353 vector magnetograms observed at HSOS, which quantitatively describe the magnetic complexity and non-potentiality. From the statistical results of the relationship between the SFP and the measures of Ls, Itot, Htot, and the sigmoid fitting curves, we can conclude that the SFP are positively correlated with the magnetic complexity and non-potentiality. This point is consistent with that of Paper I. Among Ls, Itot, and Htot, which measure is the most sensitive to the SFP? Perhaps the differential coefficient of the SFP to the measures is an evaluation criteria. Since these
Y. Cui, H. Wang / Advances in Space Research 42 (2008) 1475–1479
three measures have different units, how to rescale them into new measures with the same unit need to be further considered. In Paper I, we obtained that the productivity of higher X-ray class flares is smaller than that of lower X-ray class flares. Therefore, it is natural that the values of the SFP for P C1.0 in this study are relative larger than those values for P C5.0, M1.0, M5.0, and X1.0 flares in Paper I. Additionally, we are very interested in why the statistical relationship between solar flares and magnetic properties can be well fitted by a sigmoid function. In the next step, we should provide explanations for the physical meanings of these functions, which is beneficial to set up operational flare forecast models. References Abramenko, V. Pre-flare changes in current helicity and turbulent regime of the photospheric magnetic field. Adv. Space Res. 32, 1937–1942, 2003. Ai, G., Hu, Y. The propose for the solar magnetic field telescope and its working theorem. Publ. Beijing Astron. Obs. 8, 1–10 (in Chinese), 1986. Bao, S.D., Zhang, H.Q., Ai, G.X., Zhang, M. A survey of flares and current helicity in active regions. Astron. Astrophys. Suppl. Ser. 139, 311–320, 1999. Canfield, R.C., de La Beaujardiere, J.-F., Fan, Yuhong, et al. The morphology of flare phenomena, magnetic fields, and electric currents in active regions. I – Introduction and methods. Astrophys. J. 411, 362–369 , 1993. Cui, Y.M., Li, R., Zhang, L.Y., He, Y.L., Wang, H.N. Correlation between solar flare productivity and photospheric magnetic field properties 1. Maximum horizontal gradient, length of neutral line, number of singular points. Sol. Phys. 237, 45–59, 2006. Falconer, D.A., Moore, R.L., Gary, G.A. Correlation of the coronal mass ejection productivity of solar active regions with measures of their global nonpotentiality from vector magnetograms: baseline result. Astrophys. J. 569, 1016–1025, 2002. Falconer, D.A., Moore, R.L., Gary, G.A. A measure from line-of-sight magnetograms for prediction of coronal mass ejections. J. Geophys. Res. 108 (A10), 1380–1385, 2003.
1479
Gallagher, P.T., Moon, Y.-J., Wang, H. Active-region monitoring and flare forecasting I. Data processing and first results. Sol. Phys. 209, 171–183, 2002. Gary, G.A., Hagyard, M.J. Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity. Sol. Phys. 126, 21–36, 1990. Hagyard, M.J., Smith Jr., J.B., Teuber, D., West, E.A. A quantitative study relating observed shear in photospheric magnetic fields to repeated flaring. Sol. Phys. 91, 115–126, 1984. Leka, K.D., Barnes, G. Photospheric magnetic field properties of flaring versus flare-quiet active regions. i. Data, general approach, and sample results. Astrophys. J. 595, 1277–1295, 2003a. Leka, K.D., Barnes, G. Photospheric magnetic field properties of flaring versus flare-quiet active regions. ii. Discriminant analysis. Astophys. J. 585, 1296–1306, 2003b. Lin, Y.Z., Wei, X.L., Zhang, H.Q. Variations of magnetic fields and electric currents associated with a solar flare. Sol. Phys. 148, 133–138, 1993. McIntosh, P.S. The classification of sunspot groups. Sol. Phys. 125, 251– 267, 1990. Schmieder, B., Hagyard, M.J., Ai, G.X., Zhang, H.Q., Kalman, B., Gyori, L., Rompolt, B., Demoulin, P., Machado, M.E. Relationship between magnetic field evolution and flaring sites in AR 6659 in June 1991. Sol. Phys. 150, 199–219, 1994. Tian, L., Wang, J., Wu, D. Non-potentiality of the magnetic field beneath the eruptive filament in the bastille event. Sol. Phys. 209, 375–389, 2002. Wang, H., Ewell, M., Zirin, H., Ai, G. Vector magnetic field changes associated with X-class flares. Astrophys. J. 424, 436–443, 1994a. Wang, T.J., Xu, A., Zhang, H.Q. Evolution of vector magnetic fields and vertical currents and their relationship with solar flares in AR 5747. Sol. Phys. 155, 99–112, 1994b. Wang, J., Shi, Z., Wang, H., Lu¨, Y. Flares and the magnetic nonpotentiality. Astophys. J. 456, 861–878, 1996. Zhang, H.Q., Ai, G., Yan, X., Li, W., Liu, Y. Evolution of vector magnetic field and white-light flares in a solar active region (NOAA 6659) in 1991 June. Astrophys. J. 423, 828–846, 1994. Zhang, H.Q. Magnetic field, helicity and the 2000 July 14 flare in solar active region 9077. MNRAS 332, 500–512, 2002. Zirin, H., Liggett, M.A. Delta spots and great flares. Sol. Phys. 113, 267– 281, 1987. Zirin, H., Wang, H. Strong transverse fields in delta-spots. Sol. Phys. 144, 37–43, 1993.